The present invention relates to manufacturing and, more particularly, to the allocation of manufacturing resources in the manufacture of products.
A major challenge for manufacturing is the optimal allocation of resources to the production of multiple products when there are many choices for such allocation. Resource allocation problems need to be addressed periodically, e.g., daily, weekly, monthly, by any complex manufacturing environment. Resource allocation problems have been formalized by defining for each product a set of operations, as well as required resources for performing these operations, which must be performed for its manufacture. One formalization is referred to as the "Generalized Assignment Problem" or "GAP". In the GAP formalization, an operational cost and an operational time are assigned to the performance of a given operation on a given resource, i.e., to a given operation-resource pair. An objective, such as cost minimization, is then selected. Alternatively, assignments can be made with the objective of minimizing the total manufacturing time. More generally, both time and cost are taken into account. For example, in a "capacity-constrained resource problem", assignments can be made with the objective of minimizing cost but completing manufacturing by a certain deadline.
The generalized assignment problem has been studied very extensively. It is solvable using straight forward techniques, provided the number of variables is small or where capacity constraints are absent or so lax as to be negligible. For example, it is impracticable to solve a capacity-constrained generalized assignment problem optimally where there are, for instance, 20 or more resources, 500 or more products, an average of 10 or more operations per product, and an average of 5 or more resources compatible with each operation. Given a problem of this magnitude, a typical manufacturing deadline could pass before a computer generated the optimal solution.
A more basic problem is that the formalization of a real manufacturing situation as a generalized assignment problem is an oversimplification which can introduce considerable error between the calculated solution and the actual optimal allocation. To illustrate this, consider a situation where an operation is to be performed on a resource which has just been used to complete the previous operation for the same product. Compare this to the situation where the operation to be performed on a different but identical resource. In one case, the product is already in place for the operation to be performed, in the other case, the product must be moved and configured for the second resource. The movement incurs a cost which is not incurred when a single resource is used for successive operations. This demonstrates that the cost of performing an operation on a resource can depend on what other operations have been assigned to that resource. The generalized assignment problem does not take this dependence into account, and thus its solutions are potentially compromised. While there may be ad hoc approaches to dealing with this compromise, such methods have not provided elegant optimal or near-optimal solutions.
What is needed is an improved method for allocating manufacturing resources. The improved method should include a formalization which takes into account dependencies in the time and cost of the assignment of an operation to a resource. Specifically, the formalization should take into account dependencies of one assignment on other assignments of operations to resources. Furthermore, the method should permit problems of realistic complexity to be solved in a reasonable time using affordable computational resources.